1 Write down the names of the labelled parts of the circles below.

a ...................... d ...................... f ......................

b ...................... e ..................... g ......................

c ...................... h ......................

2 For each of these circles work out:

i the circumference

ii the area.

a i ................. b i ................. c i ................. d i .................

ii ................. ii ................. ii ................. ii .................

3 Work out the perimeter and area of the following shapes.

a b c d

...................... ...................... ...................... ......................

4 A gardener makes a circular rose bed of radius 1 m in the centre of a rectangular lawn, measuring 5 m by 4 m.

Calculate the area of the lawn after the rose bed has been made.

.........................................................................................................

5 A bicycle wheel has a circumference of 88 inches.

Calculate the radius of the wheel to the nearest inch.

.........................................................................................................

6 A circle and a square have the same area.

The square has sides of 6 cm.

Calculate the radius of the circle.

.........................................................................................................

�3 10.1 Circumference and area of a circle

281

a

bc

d

e g

h

fa

bc

d

e g

h

f

a

bc

d

e g

h

f

5 cm6 cm 18 mm 7 mm

5 cm6 cm 18 mm 7 mm

5 cm6 cm 18 mm 7 mm

5 cm6 cm 18 mm 7 mm

10 cm

8 cm

2 cm 5 cm

12 cm 14 mm

8 mm

Guided practice worksheet

D

C

Questions are targeted at the grades indicated

�3 10.2–10.3 Sectors; Problems involving circles in terms of π

283A

1 Calculate, in terms of π, the i circumference, ii area of the circles with radius or diameter given below.

a radius = 4 cm

i circumference = .................................................................

ii area = .................................................................

b radius = 32 mm

i circumference = .................................................................

ii area = .................................................................

c diameter = 7 cm

i circumference = .................................................................

ii area = .................................................................

d diameter = 9 mm

i circumference = .................................................................

ii area = .................................................................

2 Calculate the i arc length ii perimeter and iii area of each sector, correct to 3 signi� cant � gures.

a i .......................................................................... b i ..........................................................................

ii .......................................................................... ii ..........................................................................

iii .......................................................................... iii ..........................................................................

Guided practice worksheet

diameter = 12 cm(i) circumference = 2πr = 2 × π × 6 = 12π cm(ii) area = πr2 = π × 62 = 36π cm2

x 70(i) Arc length = ––––– × 2πr = ––––– × 2 × π × 8.4 = 10.26 cm (3 sf) 360 360

(ii) Perimeter = radius + radius + arc = 8.4 + 8.4 + 10.26 = 27.06 cm (3 sf)

x 70(iii) Area of sector = –––– × πr2 = ––––– × π × 8.42 = 43.1 cm2 (3 sf) 360 360

70°

8.4 cm

12°

250°130° 20°

1.2 cm

120 mm

5 cm6 mm

12°

250°130° 20°

1.2 cm

120 mm

5 cm6 mm

A

Questions are targeted at the grades indicated

D

�3 10.2–10.3 Sectors; Problems involving circles in terms of π

283B

Guided practice worksheet

c i .......................................................................... d i ..........................................................................

ii .......................................................................... ii ..........................................................................

iii .......................................................................... iii ..........................................................................

3 The diagram shows a plastic air vent.

a Calculate the area of one of the sector-shaped holes.

..............................................................................................................

b Calculate the area of plastic.

..............................................................................................................

..............................................................................................................

..............................................................................................................

4 An outdoor infrared detector senses movement up to a distance of 8 m and scans an area of 75 m2.

Calculate the angle x.

..............................................................................................................

..............................................................................................................

12°

250°130° 20°

1.2 cm

120 mm

5 cm6 mm

20°9 cm

10 cm

8 m

75 m2

x

12°

250°130° 20°

1.2 cm

120 mm

5 cm6 mm

Hint Substitute the values you know into: xArea of sector = –––– × πr2 and solve the equation 360

A*

A

�3 10.2–10.3 Sectors; Problems involving circles in terms of π

283C

Guided practice worksheet

5 Calculate, in terms of π, the i arc length ii perimeter and iii area of each sector.

a i arc length = .................................................................

ii perimeter = .................................................................

iii area = .................................................................

b i arc length = .................................................................

ii perimeter = .................................................................

iii area = .................................................................

c i arc length = .................................................................

ii perimeter = .................................................................

iii area = .................................................................

d i arc length = .................................................................

ii perimeter = .................................................................

iii area = .................................................................

4 mm

6 cm

12 m

6 mm45°

120°

10°

4 mm

6 cm

12 m

6 mm45°

120°

10°

4 mm

6 cm

12 m

6 mm45°

120°

10°

4 mm

6 cm

12 m

6 mm45°

120°

10°

A

�3 10.4 Units of area

285A

Guided practice worksheet

1 Convert the areas by multiplying.

a 0.25 m2 to mm2 b 1.4 m2 to cm2

.................................................................. ..................................................................

.................................................................. ..................................................................

c 3.4 cm2 to mm2 d 0.024 m2 to cm2

.................................................................. ..................................................................

.................................................................. ..................................................................

2 Convert the areas by dividing.

a 4500 cm2 to m2 b 34 000 cm2 to m2

.................................................................. ..................................................................

.................................................................. ..................................................................

c 320 mm2 to cm2 d 4000 mm2 to cm2

.................................................................. ..................................................................

.................................................................. ..................................................................

3 Convert the following areas by multiplying or dividing.

a 0.42 cm2 to mm2 ............................................................................................................

b 62 000 mm2 to m2 ............................................................................................................

c 237 mm2 to cm2 ............................................................................................................

d 5200 cm2 to m2 ............................................................................................................

e 0.0044 m2 to cm2 ............................................................................................................

f 0.24 cm2 to mm2 ............................................................................................................

g 350 mm2 to cm2 ............................................................................................................

h 420 000 mm2 to m2 ............................................................................................................

4 A roll of card has an area of 43 m2. A postcard has an area of 125 cm2. How many postcards can be cut from the roll, assuming there is no wastage?

......................................................................................................................................................................................................................................

Convert 0.54 m2 to mm2

1 m = 1000 mm so 1 m2 = 1000 mm × 1000 mm = 1 000 000 mm2

So 0.54 m2 = 0.54 × 1 000 000 mm2 = 540 000 mm2

Convert 3500 cm2 to m2

1 m = 100 cm so 1 m2 = 100 cm x 100 cm = 10 000 cm2 so divide by 10 000So 3500 cm2 = 3500 ÷ 10 000 m2 = 0.35 m2

Multiply if converting to a smaller unit, divide if converting to a larger unit.

C

Questions are targeted at the grades indicated

�3 10.4 Units of area

285B

5 Calculate the area of each shape in i mm2 ii cm2

a i mm2 = ........................................ b i mm2 = ........................................ c i mm2 = ........................................

ii cm2 = ........................................ ii cm2 = ........................................ ii cm2 = ........................................

6 The diameter of a 1p coin is 20.3 mm.

a Calculate its area, in mm2.

.................................................................................................................................................................................................................................

A sheet of metal measuring 33 cm by 2.6 m is used to make some coins.

b Calculate the area of the sheet, in cm2.

.................................................................................................................................................................................................................................

c Estimate the maximum number of coins that can be punched out of the sheet.

...........................................................................................................................................................................

d Calculate the area of metal sheet remaining, in cm2.

.................................................................................................................................................................................................................................

7 Lauren paints a wall in rectangular strips measuring 2.3 m by 31 cm.

a Calculate the area of a rectangular strip, in cm2.

.................................................................................................................................................................................................................................

A tin of paint covers 30 m2 when applied using a roller.

b Calculate the number of strips that Lauren can paint from a single tin.

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

Lauren’s laser measure showed that a hall wall was 8323 mm by 2341 mm.

c How many rectangular strips would cover this area?

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

Guided practice worksheet

2.35 m

6.2 mm

2 mm

1.4 m

63 cm

7 mm

4.2 cm

2.35 m

6.2 mm

2 mm

1.4 m

63 cm

7 mm

4.2 cm

2.35 m

6.2 mm

2 mm

1.4 m

63 cm

7 mm

4.2 cm

Hint Find the number of coins that would � t along each edge of the sheet.

C